Question
Solve the inequality graphically in a two-dimensional plane: y + 8 $\ge$ 2x
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Answer
The given inequality is $y + 8 \geqslant 2x$ i.e. $2x - y \leqslant 8$
Draw the graph of the line 2x - y = 8
Table of value satisfying the equation 2x - y = 8
Draw the graph of the line 2x - y = 8
Table of value satisfying the equation 2x - y = 8
| X | 5 | 6 |
| Y | 2 | 4 |
Putting (0, 0) in the given in equation, we have
$2 \times 0 - 0 \leqslant 8 \Rightarrow 0 \leqslant 8$, which is true.
$\therefore$ Half plane of $2x - y \leqslant 8$ is towards origin.
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